On two-grid convergence estimates

Robert D. Falgout; Panayot S. Vassilevski; Ludmil T. Zikatanov

doi:10.1002/nla.437

On two-grid convergence estimates

Robert D. Falgout, Panayot S. Vassilevski, Ludmil T. Zikatanov

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two-grid convergence proof of a purely algebraic 'window'-AMG method. Published in 2005 by John Wiley & Sons, Ltd.

Original language	English (US)
Pages (from-to)	471-494
Number of pages	24
Journal	Numerical Linear Algebra with Applications
Volume	12
Issue number	5-6
DOIs	https://doi.org/10.1002/nla.437
State	Published - Jun 2005

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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10.1002/nla.437

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AU - Falgout, Robert D.

AU - Vassilevski, Panayot S.

AU - Zikatanov, Ludmil T.

PY - 2005/6

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N2 - We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two-grid convergence proof of a purely algebraic 'window'-AMG method. Published in 2005 by John Wiley & Sons, Ltd.

AB - We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two-grid convergence proof of a purely algebraic 'window'-AMG method. Published in 2005 by John Wiley & Sons, Ltd.

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DO - 10.1002/nla.437

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AN - SCOPUS:22144444957

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JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 5-6

ER -

On two-grid convergence estimates

Abstract

All Science Journal Classification (ASJC) codes

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